Such circulating-ball drives have become increasingly popular in recent years, thanks to their low-friction coupling of the relatively rotatable members. It is commonly accepted that the load should be distributed as uniformly as possible among all the balls, that these balls should have substantially identical diameters and that the grooves of the spindle and the nut should be of constant cross-section throughout their lengths while being of the same pitch in both members. This has been pointed out in a comprehensive study by H. Hilmer, titled Rechnergestutzte Auslegung und Berechnung von Kugelgewindespindeln, appearing in Vol. 11 of the German series called Fertigungstechnische Berichte edited by Prof. Hans Kurt Tonshoff, published 1978 by Technischer Verlag Resch KG in the German Federal Republic.
As particularly discussed on page 79 of that publication, section 5.3.1., the stress exerted upon the balls in the several turns of the nut groove is not uniform under the aforestated conditions. According to the study, as specifically noted in sections 5.4-5.5 on pages 94-100 of that publication, a uniformization of the stress could be achieved by varying the outer diameter and thus the cross-sectional area of the nut, by modifying the flanks of the groove profile from one turn to the next in order to change the relative bending resistance of the intervening ribs, or by using balls of different diameters in the several turns (which of course calls for a separate recirculation passage for each turn). The author has found, however, that these proposed solutions are fully effective only for a limited load range; the corresponding discussion appears on pages 99-100 of the cited publication.